## Symbolic Representation

To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation.

Let's define the variables:
- $x_1$ = Number of office chairs
- $x_2$ = Number of dining chairs

The objective is to maximize profit. The profit per office chair is $120, and the profit per dining chair is $180. Therefore, the objective function can be represented as:

Maximize: $120x_1 + 180x_2$

The constraints given are:
1. The cost per office chair is $200, and the cost per dining chair is $250. The company does not want to invest more than $20,000 on chairs.
   - $200x_1 + 250x_2 \leq 20000$

2. The company estimates a monthly demand of at most 130 total chairs.
   - $x_1 + x_2 \leq 130$

Also, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of chairs cannot be negative.

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'office chairs'), ('x2', 'dining chairs')],
    'objective_function': '120*x1 + 180*x2',
    'constraints': [
        '200*x1 + 250*x2 <= 20000',
        'x1 + x2 <= 130',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Leeside_Designs_Chair_Optimization")

# Define the variables
x1 = model.addVar(name="office_chairs", lb=0, vtype=gp.GRB.INTEGER)  # Number of office chairs
x2 = model.addVar(name="dining_chairs", lb=0, vtype=gp.GRB.INTEGER)  # Number of dining chairs

# Objective function: Maximize profit
model.setObjective(120*x1 + 180*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(200*x1 + 250*x2 <= 20000, name="investment_constraint")  # Investment constraint
model.addConstr(x1 + x2 <= 130, name="demand_constraint")  # Demand constraint

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution found. Office chairs: {x1.varValue}, Dining chairs: {x2.varValue}")
else:
    print("No optimal solution found.")
```